Basic Mean-Field Theory for Bose-Einstein Condensates.- Basic Mean-Field Theory for Bose-Einstein Condensates.- Bright Solitons in Bose-Einstein Condensates.- Bright Solitons in Bose-Einstein Condensates: Theory.- Bright Solitons: Summary of Experimental Techniques.- Dark Solitons in Bose-Einstein Condensates.- Dark Solitons in Bose-Einstein Condensates: Theory.- Dark Solitons in BECs: The First Experiments.- Nonlinear Localization of BECs in Optical Lattices.- Nonlinear Localization of BECs in Optical Lattices.- Multi-Dimensional Solitons in Bose-Einstein Condensates.- Multidimensional Solitons: Theory.- Experiments on Multidimensional Solitons.- Vortices in Bose-Einstein Condensates.- Vortices in Bose-Einstein Condensates: Theory.- Vortices in Bose-Einstein Condensates: Experiments.- Vortex Lattices.- Vortex Lattices in Bose-Einstein Condensates: Theory.- Vortex Lattices in Bose-Einstein Condensates: Experiments.- Optical Lattices.- Optical Lattices: Theory.- Bose-Einstein Condensates in Optical Lattices: Experiments.- Multi-Component Bose-Einstein Condensates.- Multi-Component Bose-Einstein Condensates: Theory.- Multi-Component Condensates: Experiment.- Manipulations of Coherent Matter-Waves.- Manipulations of Coherent Matter-Waves.- Beyond Gross-Pitaevskii Mean Field Theory.- Beyond Gross-Pitaevskii Mean-Field Theory.- Asymptotic Reductions of the Gross-Pitaevskii Equation.- Asymptotic Reductions of the Gross-Pitaevskii Equation.